Good question ... which you should ask your company's immigration attorney.
Their website isn't accurate and quite often a change of status will appear and suddenly be 'changed'.
Thus, the best thing to do is stay away from their online system and look in your mailbox for the 'real' notice.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
You can continue to work until you are notified by mail that your change of status to F-1 has been approved.
Mr. Shusterman's (former INS Trial Attorney, 1976-82) response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
If your H-1B remains valid you may continue to work until notified.
Attorney Robert Brown's (former INS Director, 1972-99) reply to your question is general in nature, and does not constitute legal advice as all facts are known to him. For specific advice or representation you should retain an attorney experienced in immigration law. Mr. Brown's reply on AVVO does not create an attorney/client relationship not constitute legal advice.
The date the H-1 status ends is the last date you are legal to work as H1. There are more issues that need to be considered in this matter for a proper advice and you need specific advice so please seek private consultation.
My answers are for general information only, NOT A legal advice because these are not tailored to your specific situation. Contact an Immigration Attorney if you need legal advice.